Related papers: Stability for multivalued McKean-Vlasov stochastic…
We prove new results regarding the existence, uniqueness, (eventual) boundedness, (total) stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
We investigate existence and uniqueness of strong solutions of mean-field stochastic differential equations with irregular drift coefficients. Our direct construction of strong solutions is mainly based on a compactness criterion employing…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
We show well-posedness for McKean--Vlasov equations with rough common noise and progressively measurable coefficients. Our results are valid under natural regularity assumptions on the coefficients, in agreement with the respective…
This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove…
We examine existence and uniqueness of strong solutions of multi-dimensional mean-field stochastic differential equations with irregular drift coefficients. Furthermore, we establish Malliavin differentiability of the solution and show…
We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…
This paper proposes a notion of viscosity weak supersolutions to build a bridge between stochastic Lyapunov stability theory and viscosity solution theory. Different from ordinary differential equations, stochastic differential equations…
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
Given global Lipschitz continuity and differentiability of high enough order on the coefficients in It\^{o}'s equation, differentiability of associated semigroups, existence of twice differentiable solutions to Kolmogorov equations and weak…
As the limit equations of mean-field particle systems perturbed by common environmental noise, the McKean-Vlasov stochastic differential equations with common noise have received a lot of attention. Moreover, past dependence is an…
We investigate the well-posedness of following McKean-Vlasov equation in $\mathbb{R}^d$: \[ \mathrm{d} X_t=\sigma(t,X_t, \mu_{X_t})\mathrm{d} W_t+b(t, X_t, \mu_{X_t}) \mathrm{d} t, \] where $\mu_{X_t}$ is the law of $X_t$. The existence of…
We find some new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may have…
In this paper, we consider a class of Mckean-Vlasov stochastic differential equation with oblique reflection over an non-smooth time dependent domain. We establish the existence and uniqueness results of this class, address the propagation…
Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in…
We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the strong existence and…
We investigate discret conditions for stability and asymptotic stability by Lyapunov and the point of equilibrium of autonomous system of differential equations.